OFFSET
1,1
COMMENTS
a(17) > 10^10, if it exists. - Lucas A. Brown, Oct 09 2022
LINKS
Lucas A. Brown, A243843.py
Carlos Rivera, Puzzle 640. A sequence of semiprimes, The Prime Puzzles and Problems Connection.
EXAMPLE
The factors of 265 are 5 and 53.
The factors of 553 are 7 and 79.
The factors of 779 are 19 and 41.
The factors of 1941 are 3 and 647.
The factors of 3647 are 7 and 521.
The factors of 7521 are 3, 23, and 109.
265 is the smallest squarefree semiprime that initiates a sequence of this length, so a(5) = 265.
PROG
(Magma) lst:=[]; Factors:=func<k | Factorization(k)>; IsSemiprime:=func<k | &+[d[2]: d in Factors(k)] eq 2>; IsOK:=func<k | IsSemiprime(k) and IsSquarefree(k)>; PrimeDivisors:=func<k | &cat[[Factors(k)[j, 1]: i in [1..Factors(k)[j, 2]]]: j in [1..#Factors(k)]]>; ConcatOfPrimeDivisors:=func<k | Seqint(Reverse(&cat[Reverse(IntegerToSequence(PrimeDivisors(k)[i])): i in [1..#PrimeDivisors(k)]]))>; for n in [1..9] do k:=1; repeat k+:=1; t:=0; if IsOK(k) then b:=k; while IsOK(b) do b:=ConcatOfPrimeDivisors(b); t+:=1; end while; end if; until t eq n; Append(~lst, k); end for; lst; // Arkadiusz Wesolowski, Aug 07 2023
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Arkadiusz Wesolowski, Jun 13 2014
EXTENSIONS
Definition corrected and terms a(15) and a(16) from Lucas A. Brown, Oct 09 2022
STATUS
approved